A "full house" is a five-card hand that has two cards of the same rank and three cards of the same rank. For example, {queen of hearts, queen of spades, 8 of diamonds, 8 of spades, 8 of clubs}. How many five-card hands contain a full house?

There are 3744 of five-card hands that are indeed a full house.

Step-by-step explanation:

First, we need to select a rank that i repeated three times. There are 13 possibilities for this. Once the rank is selected, we need to select the 3 suits those cards will have. There are 4 possibilities for this (we just need to select who suit doesnt appear). So we have 13*4 = 52 possibilities to select the three cards with equal rank.

After selecting the three cards with equal rank, we need to select the rank that is repeated 2 times. We have 12 ranks left (the other one has only 1 card left), so we have 12 possibilities. Once the second rank is selected, we need to select 2 suits out of 4, which gives us possibilities. Therefore, we have 12*6 = 72 possibilities to select the two cards with equal rank.

The total amount of five-card hands containing a full house is 72*52 = 3744.

it is 570

step-by-step explanation:

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